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Are there non-trivial superperfect groups with the property that there exists a presentation of the group where the number of generators equals the number of relations? If not, is there a proof that the number of relations of non-trivial superperfect group is always greater than the number of generators?

Are there non-trivial superperfect groups with the property that there exists a presentation of the group where the number of generators equals the number of relations?

Are there superperfect groups with the property that there exists a presentation of the group where the number of generators equals the number of relations? If not, is there a proof that the number of relations of superperfect group is always greater than the number of generators?

Are there non-trivial superperfect groups with the property that there exists a presentation of the group where the number of generators equals the number of relations? If not, is there a proof that the number of relations of non-trivial superperfect group is always greater than the number of generators?